Motivation You may ask why one needs to know about quantum mechanics. Possibly the simplest answer is that we live in a quantum world! Engineers would like to make and control electronic, opto-electronic, and optical devices on an atomic scale. In biology there are molecules and cells we wish to understand and modify on an atomic scale. The same is true in chemistry, where an important goal is the synthesis of both organic and inorganic compounds with precise atomic composition and structure. Quantum mechanics gives the engineer, the biologist, and the chemist the tools with which to study and control objects on an atomic scale. As an example, consider the deoxyribonucleic acid (DNA) molecule shown in Fig. 1.1. The number of atoms in DNA can be so great that it is impossible to track the position and activity of every atom. However, suppose we wish to know the effect a particular site (or neighborhood of an atom) in a single molecule has on a chemical reaction. Making use of quantum mechanics, engineers, biologists, and chemists can work together to solve this problem. In one approach, laser-induced fluorescence of a fluorophore attached to a specific site of a large molecule can be used to study the dynamics of that individual molecule. The light emitted from the fluorophore acts as a small beacon that provides information about the state of the molecule.
Motivation You may ask why one needs to know about quantum mechanics. Possibly the simplest answer is that we live in a quantum world! Engineers would like to make and control electronic, opto-electronic, and optical devices on an atomic scale. In biology there are molecules and cells we wish to understand and modify on an atomic scale. The same is true in chemistry, where an important goal is the synthesis of both organic and inorganic compounds with precise atomic composition and structure. Quantum mechanics gives the engineer, the biologist, and the chemist the tools with which to study and control objects on an atomic scale. As an example, consider the deoxyribonucleic acid (DNA) molecule shown in Fig. 1.1. The number of atoms in DNA can be so great that it is impossible to track the position and activity of every atom. However, suppose we wish to know the effect a particular site (or neighborhood of an atom) in a single molecule has on a chemical reaction. Making use of quantum mechanics, engineers, biologists, and chemists can work together to solve this problem. In one approach, laser-induced fluorescence of a fluorophore attached to a specific site of a large molecule can be used to study the dynamics of that individual molecule. The light emitted from the fluorophore acts as a small beacon that provides information about the state of the molecule.
This introductory chapter provides an overview of quantum mechanics, which is a subject of central importance in chemistry, and is by nature a mathematical theory. The chemist's approach to the understanding of matter and its chemical transformations is to take a microscopic view, connecting experimental observation with the properties of constituent molecules. However, at the microscopic level, atoms, molecules, and their constituent particles do not obey the familiar laws of mechanics that pertain to the everyday macroscopic world. For example, the existence of molecular line spectra indicates that molecules can be found only at certain well-defined energies, unlike objects at our own scale whose energy appears to be continuously variable. This book aims to explain the fundamentals of quantum mechanics from the point of view of chemistry; describe the areas of chemistry where quantum mechanics is most important; and show how quantum mechanics is applied to chemical problems.
Introduction Key features of quantum mechanics are the uncertainty principle, wave–particle duality, quantization of energies and the modification of classical probability laws. Biology is concerned with how natural systems function – from understanding how genetically coded information is replicated, to attaining a mechanistic model for complex multistep reactions. Recently researchers have been asking whether quantum mechanics, normally the domain of physics, is also needed to understand some biological processes. This field includes fascinating developments in theory and experiment, as well as multidisciplinary discussion, and the state-of-the-art is documented in this book. Erwin Schrödinger, in his famous book What is Life ? (Schrödinger, 1944), noted that quantum mechanics accounts for the stability of living things and their cellular processes because of our understanding, via quantum mechanics, of the stability and structure of molecules. The fact that quantum effects create, sometimes large, energy gaps between different states of a chemical system is also important. Such energy gaps, between electronic energy levels, enable living organisms to capture and store the energy carried from the sun by photons, and to visualize the world around them via optically induced chemical reactions. Davydov's view in Biology and Quantum Mechanics (Davydov, 1982) was that quantum mechanics is most relevant for isolated systems in pure states and therefore is of little importance for biological systems that are in statistical states at thermal equilibrium.
The quantum world within an atom or molecule that once attracted explorations only by academic physicists now provides fertile sustenance for chemists seeking control of chemical reactions and for engineers developing ever smaller electronic devices or tools for processing information with greater security. Whereas the first pioneers could only discover the most elementary properties – the discrete energy levels that characterize the internal structures of atoms and the radiative transitions that link these structures to our external world – it is now possible to alter that structure at will, albeit briefly. Objective This monograph presents the physical principles that describe such deliberately crafted changes, namely how single atoms or molecules (or other simple quantum systems) are affected by coherent interactions, primarily laser light – a subject that has been regarded first as a part of quantum electronics and then quantum optics but is most generally described as coherent atomic excitation [Sho90]. This physics has relevance to such basic concerns as the detection and quantitative analysis of trace amounts of chemicals, the catalysis or control of chemical reactions, the alignment of molecules, and the processing of quantum information. The physics necessarily involves elementary quantum mechanics, but it has many associations to the classical dynamics that governs macroscopic objects – waves and particles. The mathematics that quantifies the changes is that of differential equations, specifically coupled ordinary differential equations (ODEs), whose parameters incorporate the controls of experimenters and whose solutions, appropriately interpreted, quantify the resulting changes.
Quantum mechanics is the basis for understanding physical phenomena on the atomic and nanometer scale. There are numerous applications of quantum mechanics in biology, chemistry and engineering. Those with significant economic impact include semiconductor transistors, lasers, quantum optics and photonics. As technology advances, an increasing number of new electronic and opto-electronic devices will operate in ways that can only be understood using quantum mechanics. Over the next twenty years fundamentally quantum devices such as single-electron memory cells and photonic signal processing systems will become common-place. The purpose of this course is to cover a few selected applications and to provide a solid foundation in the tools and methods of quantum mechanics. The intent is that this understanding will enable insight and contributions to future, as yet unknown, applications. Prerequisites Mathematics: A basic working knowledge of differential calculus, linear algebra, statistics and geometry. Computer skills: An ability to program numerical algorithms in MATLAB or similar language and display results in graphical form. Physics background: Should include a basic understanding of Newtonian mechanics, waves and Maxwell’s equations.
This modern textbook offers an introduction to Quantum Mechanics as a theory that underlies the world around us, from atoms and molecules to materials, lasers, and other applications. The main features of the book are: * Emphasis on the key principles with minimal mathematical formalism * Demystifying discussions of the basic features of quantum systems, using dimensional analysis and order-of-magnitude estimates to develop intuition * Comprehensive overview of the key concepts of quantum chemistry and the electronic structure of solids * Extensive discussion of the basic processes and applications of light-matter interactions * Online supplement with advanced theory, multiple-choice quizzes, etc.
The discovery of quantum mechanics immediately transformed both physics and chemistry, and questions were soon asked about its implications for bio- logy. The first era of quantum biology focused on the structure and stability of biological entities like molecules. A second era began in the 1960s, with lasers allowing experiments on the very short time scales relevant to atomic and mo- lecular motions. Today, we have novel nanoprobes of real living cells, and evi- dence for biological phenomena that may involve highly non-trivial quantum effects such as long-range coherence and entanglement.